How do you handle people like this?

Most likely they were discussing something they should not have done or been doing,

I would ignore it.

I think it’s more like they feel guilty about what they are doing, and don’t want anyone to think anything negative about them. They also might assume you’re like them; outwardly nice, but gossipy behind “closed doors”. Which obviously is incorrect.

I would probably mind my business and do my work unless it is something that happens repeatedly, then I might say something.

It's hard to say. I was in management a lot and so, I always made sure to tell people, if you don't want things taken "up," don't communicate those things to me, because I have liability to consider as well as obligations to report matters that may be of concern. Granted, those situations were mostly applied to things beyond mere gossip, unless it was somehow "pertinent." That being said, ALSO in management, I did not like what I called tattletales. UNLESS it was important, as in detrimental to another coworker or our production demands. I was never a tattletale inside or outside of management. But I did participate in gossip, of course. Don't we all to some degree? Were there people I KNEW were people to avoid with certain things? Certainly. Was I always right about their need to spread things around? No. Still, most people act in a manner where there is reason to suspect something. Who knows why or where they come up with the idea. Right or wrong, I guess it doesn't matter at the end of the day. I rarely paid much attention to my coworkers. I just did my job and did it the best I could, and whatever else happened just happened. It wasn't all in my control, nor did it matter to me if it was or wasn't.

I ignore it

Ignore it. It's not worth the energy. XChances are it's not about you, but their own personal insecurities. I highly doubt they think you'll report them, more they felt like they were caught with their hands in the cookie jar, and decided the conversation should've been kept behind closed doors. It's easy to think it's all about you, but you don't know that and shouldn't assume the worst. Pick your battles.

I ignore things like that.

If they were saying something malicious & untrue l would confront them about it. Gossiping is grossly unfair but l take the view that while they were gossiping about your friend they were giving others a rest! Ignore them they will be gossiping about someone else in a few minutes!